Capturing reconnection phenomena using generalized Eulerian-Lagrangian description in Navier-Stokes and resistive MHD - Cartes, Carlos and Bustamante, Miguel D. and Pouquet, Annick and Brachet, Marc E.
FLUID DYNAMICS RESEARCH 41, (2009)
Abstract : New generalized equations of motion for the Weber-Clebsch potentials
that describe both the Navier-Stokes and magnetohydrodynamics (MHD)
dynamics are derived. These depend on a new parameter, which has
dimensions of time for Navier-Stokes and inverse velocity for MHD.
Direct numerical simulations (DNSs) are performed. For Navier-Stokes,
the generalized formalism captures the intense reconnection of vortices
of the Boratav, Pelz and Zabusky (BPZ) flow, in agreement with the
previous study by Ohkitani and Constantin. For MHD, the new formalism is
used to detect magnetic reconnection in several flows: the
three-dimensional (3D) Arnold, Beltrami and Childress (ABC) flow and the
(2D and 3D) Orszag-Tang (OT) vortex. It is concluded that periods of
intense activity in the magnetic enstrophy are correlated with periods
of increasingly frequent resettings. Finally, the positive correlation
between the sharpness of the increase in resetting frequency and the
spatial localization of the reconnection region is discussed.